Astronomical Images : Lines and motions of the superior planets

Erasmus Reinhold

Astronomical Images

<p style='text-align: justify;'>This Parisian edition was copied from the first edition of the commentary of Peuerbach by Erasmus Reinhold, printed in Wittenberg by Hans Lufft in 1542. Subsequently, in 1556, Charles Perier published a new edition, copied from the revised edition printed by Lufft in 1553, which contained additions to the theory of the Sun (<i>[Theoricae] auctae novis scholiis in theoria Solis ab ipso autore</i>). This diagram, loosely based on the diagram that represents the lines and motions of the superior planets in Peuerbach's original (c. 1474) edition, is a close copy of a figure in the Wittenberg edition of Peuerbach (1535), itself copied from a figure of the Fine edition (Paris, 1525). There are similar diagrams in Reisch's <i>Margarita philosophica</i> (1503, sig. o3r) and in the Apian edition of Peuerbach (Ingolstadt, 1528; fol. 16v in our 1537 edition). Given at the end of the explanation of the motions of the superior planets, it can be used as a visual glossary. The diagram shows the three orbs of the superior planets. The outermost circle represents the ecliptic. Point A is the beginning of Aries; the eastward direction is indicated by the sequence ANMR [a misprint for K] L (<i>successio sive series Signorum ANMKL</i>). The vertical line is the line of the apogee, which passes through the apogee of the eccentric, the three aligned centres of the equant circle (H), of the eccentric (C) and of the World (D), and the perigee of the eccentric (G). The line that crosses it at right angles at the centre of the World indicates the points of the eccentric called mean longitudes (<i>longitudines mediae</i>). For a slightly different definition of the <i>longitudines mediae</i>, see fol. 57v. If the centre of the epicycle is at E, the mean apogee of the epicycle is at P; its true apogee is at O. The apogee of the eccentric 'in second signification' (<i>apogion seu aux in secunda significatione</i>) is arc AN, measured eastward (<i>versus sinistram, sive juxta ordinem Signorum</i>). The line of the mean motion (<i>linea medii motus</i>) is DL, drawn from the centre of the World to the zodiac, and parallel to line HE drawn from the centre of the equant to the centre of the epicycle. The mean motion of the epicycle or of the planet (<i>medius motus epicycli sive planetae</i>) is arc ANL. The line of the true motion of the epicycle drawn from the centre of the World to the zodiac and passing through the centre of the epicycle, is DEK according to the legend, that is DER on the diagram. The true motion of the epicycle is arc ANK (ANR on the diagram). The mean centre (<i>centrum medium</i>), that is the arc of the zodiac measured eastward from the line of the apogee to the line of the mean motion, is arc NL. The equation of the centre in the zodiac (<i>aequatio centri in zodiaco</i>), that is the arc of the zodiac between the line of the true motion of the epicycle and the line of the mean motion, is arc KL (RL on the diagram). As the centre of the epicycle is in the first half of the eccentric, it must be subtracted (<i>hic subtrahenda</i>); see fol. 54r. The true centre of the planet (<i>centrum verum sive aequatum</i>), measured on the zodiac from the line of the apogee to the line of the true motion of the epicycle, is arc NK, according to the legend, that is NR on the diagram. The body of the planet is at F, so the line of the true motion of the planet (<i>linea veri motus planetae</i>) is DFM. The mean argument of the planet (<i>argumentum medium planetae</i>), that is the arc of the epicycle measured according to the direction of the movement of this epicycle, from the mean apogee of the epicycle to the centre of the body of the planet, is the arc of the epicycle PIF. The equation of the centre in the epicycle (<i>aequatio centri in epicyclo</i>), that is the arc of the epicycle between the true and mean apogees of the epicycle, marked by two lines passing through the centre of the epicycle, the one drawn from the centre of the World (the line of the true apogee), the other from the centre of the equant (the line of the mean apogee), is arc OP. Here it must be added to the mean argument, to obtain the true argument; see fol. 54r. The true argument of the planet (<i>argumentum verum planetae</i>), that is the arc of the epicycle from the true apogee of the epicycle to the body of the planet, is arc OPIF. The equation of the argument of the planet (<i>aequatio argumenti</i>), that is the arc of the zodiac lying between the line of the true motion of the planet and the line of the true motion of the epicycle, is arc KM according to the legend, RM on the diagram. In this position of the planet, it must be subtracted. It has been explained before that when the line of the true motion of the planet precedes the line of the true motion of the epicycle (the <i>argumentum verum</i> or <i>aequatum</i> being less than 180 degrees), then the equation of the argument must be added to the true motion of the epicycle to find the true motion of the planet. On the equation of the argument of the superior planets, see fol. 57v. The true motion of the planet (<i>verus motus planetae</i>) is arc ANM. Quotations from Reinhold's commentary are translated or paraphrased by Isabelle Pantin.</p>